The partially separable functions (PSF) model is commonly adopted in dynamic MRI reconstruction, as is the underlying signal model in many reconstruction methods including the ones relying on low-rank assumptions. Even though the PSF model offers a parsimonious representation of the dynamic MRI signal in several applications, its representation capabilities tend to decrease in scenarios where voxels present different temporal/spectral characteristics at different spatial locations. In this work we account for this limitation by proposing a new model, called spatiotemporal maps (STMs), that leverages autoregressive properties of (k, t)-space. The STM model decomposes the spatiotemporal MRI signal into a sum of components, each one consisting of a product between a spatial function and a temporal function that depends on the spatial location. The proposed model can be interpreted as an extension of the PSF model whose temporal functions are independent of the spatial location. We show that spatiotemporal maps can be efficiently computed from autocalibration data by using advanced signal processing and randomized linear algebra techniques, enabling STMs to be used as part of many reconstruction frameworks for accelerated dynamic MRI. As proof-of-concept illustrations, we show that STMs can be used to reconstruct both 2D single-channel animal gastrointestinal MRI data and 3D multichannel human functional MRI data.
@article{arxiv.2507.14429,
title = {Spatiotemporal Maps for Dynamic MRI Reconstruction},
author = {Rodrigo A. Lobos and Xiaokai Wang and Rex T. L. Fung and Yongli He and David Frey and Dinank Gupta and Zhongming Liu and Jeffrey A. Fessler and Douglas C. Noll},
journal= {arXiv preprint arXiv:2507.14429},
year = {2026}
}